Question

A meter stick is found to balance at the 49.7-cm mark when placed on a fulcrum. When a 46.0-gram mass is attached at the 18.0-cm mark, the fulcrum must be moved to the 39.2-cm mark for balance. What is the mass of the meter stick?

Answer 1

A meter stick is found to balance at the 49.7-cm mark when placed on a fulcrum. When a 46.0-gram mass is attached at the 18.0-cm mark, the fulcrum must be moved to the 39.2-cm mark for balance. What is the mass of the meter stick?

$M$ - mass of the meter stick, $m = 46.0$ gram

Newton's first law for rotational motion:

$$m g l _ {1} = M g l _ {2}$$

Lengths $l_{1}$ and $l_{2}$ can be found as:

$$l _ {1} = 3 9. 2 - 1 8. 0 = 2 1. 2 \mathrm{~cm}$$ $$l _ {2} = 4 9. 7 - 3 9. 2 = 1 0. 5 \mathrm{~cm}$$

Therefore, mass of the meter stick equals:

$$M = m \frac {2 1 . 2}{1 0 . 5} = 4 6. 0 \frac {2 1 . 2}{1 0 . 5} g = 9 2. 9 g$$

Answer: $92.9g$